Single-walled carbon nanotubes (SWNTs), being hydrophobic by nature, aggregate in water to form large bundles. However, isolated SWNTs possess unique physical and chemical properties that are desirable for sensing and biological applications. Conventionally isolated SWNTs can be obtained by wrapping the tubes with biopolymers or surfactants. The binding modes proposed for these solubilization schemes, however, are less than comprehensive. Here we characterize the efficacies of solubilizing SWNTs through various types of phospholipids and other amphiphilic surfactants. Specifically, we demonstrate that lysophospholipids, or single-chained phospholipids offer unprecedented solubility for SWNTs, while double-chained phospholipids are ineffective in rendering SWNTs soluble. Using transmission electron microscopy (TEM) we show that lysophospholipids wrap SWNTs as striations whose size and regularity are affected by the polarity of the lysophospholipids. We further show that wrapping is only observed when SWNTs are in the lipid phase and not the vacuum phase, suggesting that the environment has a pertinent role in the binding process. Our findings shed light on the debate over the binding mechanism of amphiphilic polymers and cylindrical nanostructures and have implications on the design of novel supramolecular complexes and nanodevices.